Problem: Solve for $x$ and $y$ using elimination. ${2x-5y = -37}$ ${x-4y = -32}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${2x-5y = -37}$ $-2x+8y = 64$ Add the top and bottom equations together. $3y = 27$ $\dfrac{3y}{{3}} = \dfrac{27}{{3}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {2x-5y = -37}\thinspace$ to find $x$ ${2x - 5}{(9)}{= -37}$ $2x-45 = -37$ $2x-45{+45} = -37{+45}$ $2x = 8$ $\dfrac{2x}{{2}} = \dfrac{8}{{2}}$ ${x = 4}$ You can also plug ${y = 9}$ into $\thinspace {x-4y = -32}\thinspace$ and get the same answer for $x$ : ${x - 4}{(9)}{= -32}$ ${x = 4}$